Let us recall the Lax formalism of the 2D Toda hierarchy
(see the recent review [1]}).
\(t= \lbrace t_k\rbrace _{k=1}^\infty \)  and
\(\bar{t}= \lbrace \bar{t}_k\rbrace _{k=1}^\infty \) 
are the two sets of time variables.
\(s\)  is the spatial coordinate, which is understood
to be a continuous variable throughout this paper.
\(\Lambda \)  denotes the shift operator
\(\Lambda = e^{\partial _s}, \quad \partial _s = \partial /\partial s.\) 
